具有非线性标量曲率项的多维宇宙中原初黑洞的概率
Probability for Primordial Black Holes in Multidimensional Universe with Nonlinear Scalar Curvature Terms
摘要：
我们研究了具有非线性标量曲率项的多维宇宙，计算了原始黑洞的产生几率。为此，我们获得了两种不同拓扑结构的欧几里得瞬子解：（a）$S^{D-1}$ -拓扑结构，它不容纳原始黑洞和（b）$S^1\times S^{D-2}$ -拓扑结构，它容纳一对黑洞。在Hartle-Hawking边界条件的半经典近似框架下，假设引力作用量为标量曲率的多项式函数（有或没有宇宙学常数$Λ$），计算了一对黑洞的暴胀宇宙的量子产生概率.本文讨论了$R^4$ -理论中一类新的引力瞬子解，它与宇宙学模型的建立有关。
英文摘要：
We investigate multi-dimensional universe with nonlinear scalar curvature terms to evaluate the probability of creation of primordial black holes. For this we obtain Euclidean instanton solution in two different topologies: (a) $S^{D-1}$ - topology which does not accommodate primordial black holes and (b) $S^1\times S^{D-2}$-topology which accommodates a pair of black holes. The probability for quantum creation of an inflationary universe with a pair of black holes has been evaluated assuming a gravitational action which is described by a polynomial function of scalar curvature with or without a cosmological constant ($Λ$) using the framework of semiclassical approximation of Hartle-Hawking boundary conditions. We discuss here a class of new gravitational instantons solution in the $R^4$-theory which are relevant for cosmological model building.
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